Exponential Admissibility And H_∞ Filtering Of Markovian Jump Singular Systems With Saturation Actuator

This thesis is devoted to the investigation of the exponential admissibility and H_∞ filtering problem of Markovian jump systems. It includes four chapters:Chapter I is the introduction, which consists of research background, main research contents and the significant.In chapter II, a memory less feedback controller is designed for Markovian jump stochastic singular bilinear systems with saturating actuators and general unknown transition probabilities, and the constraint and the time delay in the input control are taken into account. Based on Lyapunov-Krasovskii theory and enlargement of matrix inequality, a sufficient condition is derived from the exponential admissibility in meansquare of delayed Markovian jump stochastic singular bilinear systems with saturating actuators and general unknown transition probabilities. A numerical example is provided to demonstrate the effectiveness of the results.In chapter III, the investigation of the problem of delay-dependent H_∞ filtering for a kind of singular Markovian jump time-delay systems with general unknown transition probabilities is investigated. In this model, each transition rate can be completely unknown or only its estimate value is known. Using the Lyapunov functional theory, a stochastically stable filter is designed to guarantee both the mean-square exponential admissibility and a prescribed level of H_∞ performance for the singular Markovian jump time-delay systems with general unknown transition probabilities. A sufficient condition is derived from the existence of such a desired filter in terms of linear matrix inequalities(LMIs). A numerical example is provided to demonstrate the effectiveness of the proposed theory.The uncertain transition probabilities discussed in this paper can be completely unknown, or only the range of transition probability is known. A special matrix is established to link the switching between different modes. The numerical example shows the effectiveness of the proposed method.